Dynamics of a stochastic SIR epidemic model driven by Lévy jumps with saturated incidence rate and saturated treatment function
Amine El Koufi, Jihad Adnani, Abdelkrim Bennar, Noura Yousfi
Abstract
In this article, we consider a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Lévy noise. First, we prove the existence of a unique global positive solution to the model. We investigate the stability of the free equilibria E0 by using the Lyapunov method. We give sufficient conditions for the persistence in the mean. We show the dynamic properties of the solution around endemic equilibria point of the deterministic model. Moreover, we display some numerical results to confirm our theoretical results.
Topics & Concepts
MathematicsEpidemic modelLyapunov functionStability (learning theory)Function (biology)Applied mathematicsIncidence (geometry)Persistence (discontinuity)Nonlinear systemDemographyGeometryComputer scienceEngineeringGeotechnical engineeringSociologyQuantum mechanicsEvolutionary biologyBiologyPopulationMachine learningPhysicsMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Differential Equations AnalysisCOVID-19 epidemiological studies